Comparative Study of Dual-Stator Permanent Magnet Machines with Different PM Arrangements and Rotor Topologies for Aviation Electric Propulsion ^†

Abstract

The dual-stator permanent magnet (DSPM) machine has proved to have high space utilization and a redundant structure, which can be beneficial to improving the fault tolerance and torque density performance. In this paper, three types of DSPM machines are proposed and compared, where two sets of armature windings are wound in both inner/outer stators, producing more than one torque component compared with single-stator PM machines. The machine topology and operating principle of three DSPM machines are analyzed first. Next, feasible stator/rotor-pole number combinations are compared and determined. Furthermore, based on the finite-element (FE) method, both the electromagnetic performances of three DSPM machines under open-circuit and rated-load conditions after optimization are compared, aimed at generating maximum torque at fixed copper loss. The FE analyses indicate that the dual-stator consequent-pole permanent magnet (DSCPPM) machine generates maximum torque per PM volume, together with relatively high efficiency, which makes it a potentially hopeful candidate for low-speed and high-torque applications. In addition, a thermal analysis is carried out to confirm the validity of the design scheme. Finally, in order to verify the FE predictions, a prototype DSCPPM machine is manufactured and experimentally tested.

1. Introduction

Benefitting from the rapid development of rare earth materials, permanent magnet (PM) machines have become widely applied in many fields owing to their high torque density and efficiency [1,2]. In addition, growing attention has also been paid to high reliability and high torque density in certain situations, such as the aviation electric propulsion [3,4].

As a key technology in the development of all-electric and more-electric aircraft, electric actuation systems focus on high reliability, high power density, and high efficiency in aviation electric propulsion machines. The reliability of aircraft propulsion machines is directly tied to the safety of both flight operations and passengers. Any failure could lead to significant economic and social repercussions, which makes reliability and fault tolerance the primary considerations. Additionally, to enhance aircraft payload capacity and reduce overall weight, aviation electric propulsion systems should also exhibit high power and torque density [5,6].

However, achieving both high torque/power density and high reliability in electric machines often proves challenging. On the one hand, higher power and torque density typically require the machine to operate under elevated electromagnetic loads, which can introduce reliability concerns such as insulation degradation and demagnetization risks [7]. On the other hand, enhancing motor system reliability and fault tolerance is commonly achieved through modular stator design, redundant structures, or multi-phase winding configurations [8,9]. In addition, as the number of motor phases increases, the cost and complexity of the drive system increase as well, which proportionally raises the probability of faults occurring in each module. Additionally, redundant and fault-tolerant designs can inherently compromise the motor system’s power and torque density.

From the perspective of machine topology, axial permanent magnet motors hold unique advantages in numerous applications due to their high torque density and compact structural design [10,11]. For example, the low-speed machines with axial flux can be suitable for direct-drive wind power generators. However, the radial permanent magnet motors could be advantageous when facing high-speed situations. In addition, the technological maturity, assembly difficulty, and lower R&D costs [12,13] for radial permanent magnet motors may also be superior to those of axial permanent magnet motors [14,15].

Thus, the radial flux dual-stator PM machines [16,17] could be expected as a promising candidate for aviation electric propulsion systems [18,19]. The outer and inner stators of dual-stator permanent magnet (DSPM) machines are equipped with three-phase windings, which produce the electromagnetic torque together. Therefore, higher unit power capacity can be achieved within a limited space and total amount of PM material.

As the magnet is mostly embedded in the rotor for DSPM machines, the rotor configuration plays a significant role. Generally, different rotor topologies have their pros and cons, respectively. The assembly for a regular surface-mounted structure is relatively simple, but the torque transfer ability and mechanical strength are relatively low [20]. For spoke-type rotor structure [21,22], each pole has larger magnetic flux and higher mechanical strength; however, its assembly process can be complicated. For the consequent-pole rotor structure [23,24], the consumption of PM is reduced compared with the regular surfaced-mounted structure, which may be helpful to improve the utilization rate of PM materials and save costs. Nevertheless, unbalanced magnetic force (UMF) may be caused by an asymmetric rotor structure and increase the torque ripple and vibration as a result [25]. But these different types of rotor topology and PM arrangements have not been compared and investigated in DSPM machines. In addition, compared with single-stator permanent magnet machines, DSPM machines are more flexible in topology and winding structure, which has not been comprehensively investigated in most existing studies [26]. However, the thermal analysis and further experimental tests (including cogging torque and on-load static torque performances) were not investigated, which will be studied and performed in this paper.

In this article, a novel dual-stator consequent-pole permanent magnet (DSCPPM) machine is proposed to further improve the torque density and torque/PM ratio. Comprehensive analyses and comparisons of the electromagnetic performances among these three DSPM machines with different rotor topology and PM arrangements have been carried out by using the finite-element (FE) method, which makes it beneficial to establish design criteria for DSPM machines. Moreover, a DSCPPM prototype machine has been manufactured, and the FE analyses have been confirmed.

2. Machine Topology

The main structure of three investigated DSPM machines with different rotor topologies (regular, spoke-type, and consequent-pole) is presented in Figure 1, respectively. In this section, the 12-slot/10-pole combination is selected for comparative analysis. It can be seen from Figure 1 that the outer/inner stator structure (including the stator/rotor-pole number combination) and armature winding are exactly the same, where the key difference is the rotor configuration.

In addition, the detailed configuration of inner/outer stator windings is presented in Figure 2, where all of the aforementioned DSPM machines share the same stator star of slots. Since the number of stator slots per pole is 6/5, the nonoverlapping winding coils are employed. Figure 2a shows the distribution of stator coils in mechanical degrees. The stator coil back-EMF phasors are calculated as shown in Figure 2b, where coils numbered 1, 2, 7, and 8 belong to phase A, coils numbered 3, 4, 9, and 10 belong to phase B, and coils numbered 5, 6, 11, and 12 belong to phase C.

For the sake of fair comparison, the outer/inner stator diameter, axial length, air-gap length, rotation speed, slot fill factor, and winding configurations are fixed during the optimization. It should be noted that during the optimization process, the copper losses for different rotor topologies are the same considering the thermal management and temperature rise limit. In addition, with the purpose of maximum torque and torque/PM ratio, the DSPM machines composed of three different rotor structures are globally optimized by using the FE method, where the optimization is related to the comparison of pre- and post-optimization results. The optimization variables include PM thickness, split ratio, stator tooth width, yoke thickness, slot shape, etc. After several iterations, the optimal structures of three DSPM machines can be obtained, and their optimized parameters are listed in

Table 1. Main parameters of three optimized DSPM machines.

Parameters	Regular-Type	Spoke-Type	Consequent-Pole
Number of slots, Ns	12	12	12
Number of pole pairs, P	5	5	5
Stator inner radius, Ri Stator outer radius, Ro	25 mm	25 mm	25 mm
	100 mm	100 mm	100 mm
Outer/inner air-gap length, go/gi	1.6 mm	1.6 mm	1.6 mm
Rated speed	500 rpm	500 rpm	500 rpm
Rated voltage	≤110 V	≤110 V	≤110 V
Power level	≥1.5 kW	≥1.5 kW	≥1.5 kW
Copper loss	60 W	60 W	60 W
Winding turns/wire type	100 turns/standard round wire
Magnet remanence, Br	1.2 T
Outer stator bore, Rso	78 mm	82 mm	78 mm
Inner stator bore, Rsi	64.8 mm	56.8 mm	63.8 mm
Outer tooth width, Two	13 mm	12 mm	13 mm
Inner tooth width, Twi	11 mm	10 mm	10 mm
Rotor thickness, hm	10 mm	22 mm	11 mm
Outer slot bottom, Rsbo	93.5 mm	94 mm	93.5 mm
Inner slot bottom, Rsbi	30.5 mm	30 mm	30 mm
Magnetization	Radial	Tangential	Radial
Outer/inner slot opening angle, boao/boai	16 deg.	15 deg.	15 deg.

.

3. Electromagnetic Performance

In this section, both the open-circuit and on-load electromagnetic performances of DSPM machines with different rotor topologies (including regular, spoke-type, and consequent-pole) are analyzed and compared. As the N35UH PM material has the key characteristics of high magnetic properties (maximum energy product) and high-temperature stability, the N35UH magnets are applied and investigated in this paper.

Figure 3 shows the open-circuit flux density and flux line distributions for DSPM machines with different rotor topologies after optimization. It can be observed clearly that the size parameters of the optimized regular structure and the consequent-pole structure are roughly the same, while the rotor thickness of the spoke-type structure is relatively larger. Moreover, although the amount of permanent magnet in the consequent-pole structure is nearly half of that in the regular structure, its flux density is not significantly reduced.

Harmonic distortion refers to the deviation of the magnetic flux waveform from an ideal sinusoidal shape, generating higher-order harmonics; thus, its critical impacts on machine design can be summarized as reduced efficiency, torque ripple, and reliability risks, etc. To further compare the electromagnetic performances of three DSPM machines, the detailed open-circuit and on-load results are carried out as described below.

3.1. Open-Circuit Phase Flux Linkage

The comparisons of open-circuit phase flux linkage waveforms and spectra are presented in Figure 4, where all three machines have bipolar and sinusoidal phase flux linkage, since the dc and even harmonic components are eliminated by reversely connecting the coils differing by 180 electrical degrees.

It can also be observed that the regular DSPM machine has the highest amplitude of phase flux linkage, which is 9.3% and 12.9% higher than the spoke-type/consequent-pole structure, respectively.

The open-circuit phase flux linkage spectra show that spoke-type DSPM machine has the largest total harmonic distortion (THD) among the three investigated DSPM machines.

3.2. Phase Back-EMF

Figure 5 shows the comparisons of phase back-EMF waveforms and spectra of DSPM machines with different rotor topologies at 500 r/min, respectively. It can be indicated that the phase back-EMF for three DSPM machines is not ideally sinusoidal because the odd harmonics are not negligible, especially the third harmonic.

For the fundamental component, the regular DSPM machine has the largest fundamental wave amplitude (about 101.4 V), where that of spoke-type and consequent-pole structures are 7.9% and 18.3% lower than the regular structure.

For odd harmonic components, it is obvious that the 5th and 7th harmonics of phase back-EMF can be neglected. In addition, the odd harmonics are mainly dominated by the third harmonic, and the consequent-pole and regular structures have nearly identical third harmonic components, which are about 50% lower than that in the spoke-type structure.

Since the third harmonic in line back-EMF can be eliminated by applying the star winding connection, the odd harmonics of back-EMF hardly generate torque harmonics when input phase currents are sinusoidal. In addition, the THD coefficient (excluding third harmonic) of phase back-EMF can be calculated as 4.64%, 3.48%, and 5.92% for consequent-pole structure, regular structure, and spoke-type structure, respectively.

3.3. Cogging Torque

The mechanical period angle of one cogging torque cycle can be deduced as:

$${\theta }_c={\displaystyle \frac{360}{LCM(Z,2p)}}$$

(1)

where θ_c is the mechanical angle of a cogging torque per period, LCM denotes the least common multiple. As the slot–pole combination investigated in this paper is 12/10, the θ_c can be calculated as 6 degrees.

The comparisons of the cogging torque waveforms of three DSPM machines are presented in Figure 6.

As can be seen, the consequent-pole DSPM machine has the smallest cogging torque among the three investigated rotor topologies, which is only 0.26 Nm. In addition, the cogging torque of a regular DSPM machine is about 0.57 Nm, whereas the spoke-type DSPM machine has the largest cogging torque (around 1.35 Nm).

3.4. Electromagnetic Torque

According to the basic optimized parameters shown in Table 1, the comparisons of rated torque waveforms for three DSPM machines are investigated, and the torque control (field-oriented control strategy) is adopted in this article, where the direct-axis current i_d is set to zero.

The rated torque waveforms of DSPM machines with different rotor topology are compared in Figure 7. It is indicated that the regular DSPM machine has the largest average torque (around 29.7 Nm), and the average torque of the consequent-pole structure is around 25.3 Nm. In addition, the spoke-type DSPM machine has the lowest rated torque, which is 19% lower than the regular structure.

In addition, the harmonic analysis for the waveforms of electromagnetic torque is also analyzed and presented in

Table 2. Harmonic analysis for electromagnetic torque.

Parameters	Regular	Spoke-Type	Consequent-Pole
DC component of torque (Nm)	29.12	24.08	25.31
THD of AC torque component (%)	3.03	5.62	3.95

, where the DC components of electromagnetic torque are 29.12 Nm, 24.08 Nm, and 25.31 Nm for regular, spoke-type, and consequent-pole structures. At the same time, the THD of AC torque components can be calculated as 3.03%, 5.62%, and 3.95%, respectively.

Due to different topologies, the main design parameters (including rotor thickness, slot area, etc.) of three optimized DSPM machines are unequal, where the consumption of PM materials varies as well. Therefore, selecting the average rated torque value as the single optimization objective is not entirely reasonable. As the high-performance PM material consumption is one of the main costs in the actual machine manufacturing process, the torque/PM ratio (output torque generated by unit PM) is considered in this article as well.

Figure 8 shows the comparisons of average torque and torque/PM ratio of three DSPM machines under rated-load condition. Although the average torque for a consequent-pole DSPM machine is 14% lower than a regular structure, the consequent-pole DSPM almost reduces the consumption of PM material in half. Therefore, it is noticeable that the consequent-pole DSPM machine performs best with regard to torque/PM ratio (around 206.5 kN/m³), which is far better than other topology types. As a contrast, the spoke-type DSPM machines have the second-highest torque/PM ratio (around 145.8 kN/m³), while the regular structure has the lowest torque/PM ratio (only 132.4 kN/m³).

In order to have a more comprehensive analysis and comparison of the three investigated DSPM machines, other electromagnetic performances are performed in

Table 3. Electromagnetic performance comparisons.

Parameters	Value
	Regular	Spoke-Type	Consequent-Pole
Rotation speed	500 rpm
Copper loss	60 W
Average torque	29.7 Nm	24.1 Nm	25.3 Nm
Peak-to-peak torque ripple	2.04 Nm	2.74 Nm	2.36 Nm
Torque/PM ratio	132.4 kN/m3	145.8 kN/m3	206.5 kN/m3
PM eddy current loss	53.1 W	0.72 W	18.3 W
Outer stator iron loss	9.8 W	8.37 W	8.08 W
Inner stator iron loss	5.91 W	7.14 W	5.59 W
Output power	1555.1 W	1261.9 W	1324.7 W
Efficiency	92.4%	94.1%	93.5%

. The copper loss is fixed at 60 W due to thermal management and temperature rise limit. It can be seen that the PM eddy current loss is the main difference among the three DSPM machines. By comparison, the spoke-type DSPM machine has the lowest eddy current loss, which can almost be neglected, as the spoke-type structure embed magnets within the rotor core; the reluctance torque and optimized rotor design can be utilized to suppress magnetic field harmonics, thereby reducing eddy current losses. In contrast, the regular DSPM machine has the highest PM eddy current loss (around 53.1 W), as the regular surface-mounted structure has magnets directly attached to the rotor surface, where exposure to strong alternating magnetic fields may lead to higher eddy current losses. Moreover, the consequent-pole DSPM machine has the lowest stator iron loss, while the regular DSPM machine behaves worst.

In general, through comprehensive contrast, it can be summarized that the regular DSPM machines have the highest average torque and output power, while their torque/PM ratio is the lowest. Furthermore, the PM eddy current loss and stator iron loss for a regular DSPM machine are the highest, which leads to the lowest efficiency as well. As far as the spoke-type DSPM machine is concerned, it has the highest efficiency due to low eddy current/iron loss; however, it performs worse in average torque and torque ripple. At the same time, the torque/PM ratio of the spoke-type DSPM machine is relatively low, which is only about 10% higher than the regular DSPM machines.

For the consequent-pole DSPM machine, it has the highest torque/PM ratio, which is about 56% higher than regular DSPM machines. In addition, although its torque and efficiency are not the highest, they are both close to the highest value.

To sum up, the proposed DSCPPM machine enjoys the highest torque/PM ratio, together with relatively high average torque and efficiency, which can be the potential optimal choice.

4. Thermal Analysis

Compared with conventional single-stator PM machines, the exciting current exists in both the inner and outer stator for the DSPM machine. In addition, the consequent-pole DSPM machine generates relatively high PM eddy current loss according to the electromagnetic analysis before.

In practice, the outer stator is connected with the housing, and the inner stator is not connected with the casing, where the heat dissipation for the inner stator is mostly distributed outward through the end cover and rotating shaft. Since the rotor is located between the inner and outer stators, the heat of the rotor is mainly dissipated outward through the rotating shaft, which makes it difficult to dissipate heat inherently.

In order to avoid potential risk of insulation damage and demagnetization caused by temperature rise for the rotor and inner armature winding, it is necessary to carry out thermal analysis for the proposed DSCPPM machine.

For simplicity of calculation, the following assumptions are considered during the thermal analysis: (1) the heat source of the machine is uniformly distributed in each part; (2) the insulation material inside the armature winding and stator slot is uniformly distributed; (3) the radiation heat transfer effect inside the machine is negligible; (4) the influence of air (except for the air gap) on temperature is negligible.

Based on the simplification assumed above and considering the periodicity of the circumferential direction of the DSCPPM machine structure, a circumferential 1/12 model is established in this paper to perform thermal analysis. The plot mesh of the DSCPPM machine thermal model is presented in Figure 9, where the inner/outer stator end windings are simplified as well.

Detailed thermal properties of used materials are listed in Table 3. To simplify the modeling process without sacrificing accuracy, the winding, stator core, and rotor assembly are treated as individual components with anisotropic thermal conductivity. The composite thermal conductivity values are given in

Table 4. Thermal properties of the different materials.

Components	Materials	Thermal Conductivity (W/m/K)	Heat Capacity (J/kg/K)
Housing/End caps	Aluminum	202.4	880
Winding	Copper	387	390
	Insulation	0.2	1800
Magnet	N35UH	9	500
Stator iron	35WW400	34	710
Rotor sleeve	Steel	14.9	460
Airgap	Air	0.03	1000

, which are calculated according to their exact geometries and dimensions. The heat source is referred to in the loss distribution shown in Table 2. The thermal boundary, which considers a combination of natural convection and external radiation, is specified for the outer wall of the housing and endcaps as given in

Table 5. Composite thermal conductivity values of the machine.

Components	Radial Thermal Conductivity (W/(m·K))	Circumferential Thermal Conductivity (W/(m·K))	Axial Thermal Conductivity (W/(m·K))
Winding	0.59	0.59	260
Stator iron	34	34	0.97
Rotor	21.5	14.2	4.99

. Thus, the heat generated in the DSCPPM is transferred between the machine components and is eventually dissipated to the ambient from the above boundaries.

The heat dissipation condition is shown in

Table 6. Heat dissipation condition.

Ambient temperature	20 °C
Flow heat transfer coefficient of housing outer wall	5.5 W/(m2·K)
Emissivity of housing outer wall	0.9
Flow heat transfer coefficient of endcaps outer wall	6.7 W/(m2·K)
Emissivity of endcaps outer wall	0.9

, based on the above assumptions of modeling, boundary conditions, heat source distribution, and the ambient temperature set to 20 °C, the temperature distribution of the proposed DSCPPM machine can be calculated as shown in Figure 10.

It can be noticed that the highest operating temperature occurs in the inner stator winding near the air gap because the inner stator winding mainly dissipates heat to the shaft through heat conduction, while the inner stator winding near the air gap is the furthest from the shaft. In addition, the temperature of the outer stator winding is lower than that of the inner stator winding, which is mostly due to the fact that the heat dissipation condition of outer stator winding (directly connected to the housing) is better than that of the inner stator winding. On the whole, the temperature rises in each part of the DSCPPM machine are within the permissible range (E-class winding insulation), which confirms the validity of the design scheme. More effective cooling on the inner stator side is desired to reduce the hotspot of the high temperature in the future. In addition, the internal magnet topology could raise the mechanical failure risk when the rotation speed is high. However, the rated speed in this paper is 500 rpm; thus, the mechanical failure risk may not be the main focus issue in this paper, which will be investigated in further research.

5. Experimental Test

In order to verify the theoretical analysis of electromagnetic performances in the previous section, a 12-slot, 5-pole DSCPPM prototype machine has been designed and fabricated, where the major parameters are listed in Table 2. In addition, Figure 11 shows the outer/inner stator lamination, consequent-pole rotor, and the assembled prototype, respectively, where two sets of armature windings are wound in the outer/inner stator.

It can also be seen that there are five permanent magnets arranged in the rotor iron. The shape of the permanent magnet is tile-shaped, and the PM material is N35UH, where the magnetization direction of the prototype is uniformly outward. It should be noted that in order to reduce eddy current loss, the rotor iron is also laminated, where the iron core material is 35WW400.

In addition, the rotor iron and permanent magnet are placed in a circular rotor sleeve to enhance its mechanical strength, and the material of the rotor sleeve is stainless steel.

Based on the measuring technique introduced in [27], the experimental testing platform for measuring cogging torque/static torque can be established as shown in Figure 12, where the DSCPPM prototype is clamped by three jaws. During the testing process, the balance bar attached to the prototype shaft is adjusted to be horizontal. By controlling the indexing head, the rotor rotates to correspond to different positions. In addition, the armature windings are excited with fixed dc current by the dc power supply, and the static torque can be calculated on the basis of the display of the digital scale.

During the cogging torque test of the DSCPPM prototype, both the inner and outer stator windings are open circuit. By rotating the consequent-pole rotor to different positions, the comparisons of FE-predicted and measured cogging torque waveforms are presented in Figure 13a. Additionally, the spectrums for experimentally measured cogging torque waveforms are presented in Figure 13b.

During the cogging torque test of the DSCPPM prototype, both the inner and outer stator windings are open circuit. By rotating the consequent-pole rotor to different positions, the comparisons of FE-predicted and measured cogging torque waveforms are presented in Figure 13. It can also be seen that the period of measured cogging torque is in excellent agreement with the FE-predicted period (6 mechanical degrees), but there exists certain asymmetry in the positive and negative half-cycle waveforms of measured cogging torque. Through observation and analysis, the actual mechanical air gap is small due to the rotor sleeve of the prototype; there also exist certain errors during the manufacturing process of the permanent magnet.

As the cogging torque amplitude of the DSCPPM prototype is small, only about 0.6 Nm, the experimental measured values of electromagnetic performances are in good agreement with the FE predictions on the whole.

Except for the cogging torque test, the prototype static torque is also tested in this paper. Using the dc power supply, the three-phase armature windings are energized with dc current, i.e., Ia = −2Ib = −2Ic, where Ia, Ib, and Ic are the amplitudes of three-phase current. The prototype was rotated for one electrical cycle by shaking the indexing dial, and the static torque can be recorded at different rotor positions.

Figure 14a shows the comparisons of FE-predicted and measured static torque waveforms of the prototype. It can be seen that the amplitudes of FE-predicted and measured static torque are 10.9 Nm and 9.6 Nm, respectively, where the measured static torque is slightly lower than the FE results (around 10%). Considering the fact that the FE simulation does not take end effect into account and there also exists error in the process of prototype fabrication, assembly, and testing. For example, the knife-cutting technology is applied, which may cause larger errors in comparison with laser cutting. In addition, the uneven air gap during the assembly process may also increase the torque ripple and decrease the torque/efficiency shown in Figure 13 and Figure 14. During the testing process, the temperature distribution is within the permissible range, where the prototype losses are acceptable as well. In general, the experimental static torque tests are in great agreement with previous FE simulations. Additionally, the spectrums for experimentally measured static torque waveforms are presented in Figure 14b.

In addition, in order to further verify the prototype, the comparisons of FE-predicted and measured static torque waveforms with variation in input current are presented in Figure 15. It can be seen that the measured static torque is almost proportional to the input current. At the same time, the maximum error between FE predictions and measured results is within 5%, which strongly verifies the feasibility of the proposed prototype.

6. Conclusions

In this article, a novel DSCPPM machine was presented, and three DSPM machines with different types of rotor topologies were investigated and comprehensively compared based on the FE method.

The novel DSCPPM machine exhibits high back-EMF, low cogging torque, together with minimal harmonic distortion in comparison with spoke-type rotor structure and regular rotor structure. In addition, the novel DSCPPM machine enjoys the highest torque/PM ratio (over 50% higher than the other two rotor structures), together with relatively high efficiency, which could be a tradeoff taking output power, efficiency, cost, and torque ripple into account. Additionally, this paper provides a multi-dimensional comparison of dual-stator permanent magnet synchronous motors (PMSMs) with different rotor configurations, supported by experimental validation, offering insights for the optimization of radial DSPM machines in future research.